Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I have a vector A. I want to re-index vector A.

After re-indexing it, I will use the elements of the vector in new calculations.

For example:

 

k:=2:
M:=3:
A:=Vector[column]([seq(seq(p*q,q=0..M-1),p=1..2^(k-1))]);
C:=Vector[column]([seq(seq(c(p,q),q=0..M-1),p=1..2^(k-1))]); 
Equate(C,A);
c(1,0)+c(2,1);

c(1,0)+c(2,1)=2.

But the above code doesn' t work.

How I can solve algebraic differential equation of index 2 in Mae 15?

I have modeled a simple pendulum with large intital amplitude (so we do not approx sin(theta) by theta).

I have a plot of theta agains time but would like to have both theta (position) and theta' (velcocity) on same graph.

Grateful for any suggestions

Pendulum2time.mw
 

Simple pendulum without approximating sin(θ) to θ

restart; with(DEtools)

ode := diff(theta(t), t, t)+g*sin(theta(t))/L = 0; ics := theta(0) = 1, (D(theta))(0) = 0

diff(diff(theta(t), t), t)+g*sin(theta(t))/L = 0

 

theta(0) = 1, (D(theta))(0) = 0

(1)

g := 9.8; L := .75

ans := dsolve({ics, ode}, theta(t), numeric, output = Array([0, .1, .2, .3]))

Matrix(%id = 18446746279246469110)

(2)

NULL

DEplot(ode, theta(t), t = 0 .. 3.5, theta = -1 .. 1, [{ics}], linecolour = blue)

 

with(plots); odeplot(dsolve({ics, ode}, theta(t), numeric), t = 0 .. 3.5, colour = blue)

 

NULL


 

Download Pendulum2time.mw

 

In the uploaded worksheet a block slides up the Hill from an initial position at an initial horizontal velocity. The block's motion is subject to sliding friction.

How can the equations of the block's motion be obtained to include the effects of gravity and friction?

It may simplify the answer to end the block's upward motion when gravity and friction bring it to an instantaneous halt.

Block_sliding.mw

Hello,

I am currently using NonliearFit to curve fit my data. 

The problem is that If I use a very long function that I should use for my project,

an error message appears as shown below.

The equation seems OK since I can plot them when parameters are set to certain values.

And if I use a simple equation NonlinearFit works fine. 

I will appreciate your helpful comments. Thank you!

-----------------------------------------------------Nonlinear_Fit_Complex_Equation.mw
 

restart 

with(Statistics) 

  X1 := Vector([0, 1, 2, 3, 4, 5, 6, 7, 8], datatype = float)

Y1 := Vector([0, -0.18e-1, -0.36e-1, -0.44e-1, -0.49e-1, -0.51e-1, -0.52e-1, -0.54e-1, -0.54e-1], datatype = float)

k__plot := proc (beta, k, t) options operator, arrow; [.1544730161*beta*(Sum((-1)^n*exp(-10000000000*Pi^2*(1+2*n)^2*k*t)*(-(1/2)/sqrt(Pi)+(1/2)*cos((1/2)*(1+2*n)*Pi)/sqrt(Pi)+(1/4)*sqrt(Pi)*(1+2*n)*sin((1/2)*(1+2*n)*Pi))/((2*Pi*n+Pi)*(1+2*n)^2), n = 0 .. infinity))+(-1)*0.1343994407e-1*beta+(-1)*0.6807477066e-1*beta*(9.869604401+8.*(Sum(-exp(-10000000000*Pi^2*(1+2*n)^2*k*t)/(1+2*n)^2, n = 0 .. infinity)))] end proc

plot0 := plot(k__plot(0.78e-1, 3*10^(-12), t), t = 0 .. 20)

 

``

``

[.1544730161*beta*(Sum((-1)^n*exp(-10000000000*Pi^2*(1+2*n)^2*k*t)*(-1/(2*sqrt(Pi))+cos((1/2)*(1+2*n)*Pi)/(2*sqrt(Pi))+(1/4)*sqrt(Pi)*(1+2*n)*sin((1/2)*(1+2*n)*Pi))/((2*Pi*n+Pi)*(1+2*n)^2), n = 0 .. infinity))-0.1343994407e-1*beta-0.6807477066e-1*beta*(9.869604401+8.*(Sum(-exp(-10000000000*Pi^2*(1+2*n)^2*k*t)/(1+2*n)^2, n = 0 .. infinity)))]

[.1544730161*beta*(Sum((-1)^n*exp(-10000000000*Pi^2*(1+2*n)^2*k*t)*(-(1/2)/Pi^(1/2)+(1/2)*cos((1/2)*(1+2*n)*Pi)/Pi^(1/2)+(1/4)*Pi^(1/2)*(1+2*n)*sin((1/2)*(1+2*n)*Pi))/((2*Pi*n+Pi)*(1+2*n)^2), n = 0 .. infinity))-0.1343994407e-1*beta-0.6807477066e-1*beta*(9.869604401+8.*(Sum(-exp(-10000000000*Pi^2*(1+2*n)^2*k*t)/(1+2*n)^2, n = 0 .. infinity)))]

(1)

  NonlinearFit([.1544730161*beta*(Sum((-1)^n*exp(-10000000000*Pi^2*(1+2*n)^2*k*t)*(-(1/2)/Pi^(1/2)+(1/2)*cos((1/2)*(1+2*n)*Pi)/Pi^(1/2)+(1/4)*Pi^(1/2)*(1+2*n)*sin((1/2)*(1+2*n)*Pi))/((2*Pi*n+Pi)*(1+2*n)^2), n = 0 .. infinity))-0.1343994407e-1*beta-0.6807477066e-1*beta*(9.869604401+8.*(Sum(-exp(-10000000000*Pi^2*(1+2*n)^2*k*t)/(1+2*n)^2, n = 0 .. infinity)))], X1, Y1, t)

Error, (in Statistics:-NonlinearFit) invalid input: no implementation of NonlinearFit matches the arguments in call, 'NonlinearFit([.1544730161*beta*(Sum((-1)^n*exp(-10000000000*Pi^2*(1+2*n)^2*k*t)*(-(1/2)/Pi^(1/2)+(1/2)*cos((1/2)*(1+2*n)*Pi)/Pi^(1/2)+(1/4)*Pi^(1/2)*(1+2*n)*sin((1/2)*(1+2*n)*Pi))/((2*Pi*n+Pi)*(1+2*n)^2), n = 0 .. infinity))-0.1343994407e-1*beta-0.6807477066e-1*beta*(9.869604401+8.*(Sum(-exp(-10000000000*Pi^2*(1+2*n)^2*k*t)/(1+2*n)^2, n = 0 .. infinity)))], op(w), t)'

 

``

NonlinearFit(beta+4*t+5*exp(k*t), X1, Y1, t)

-HFloat(17.773016167748086)+4*t+5*exp(-HFloat(0.37019659804002825)*t)

(2)

``


 

Download Nonlinear_Fit_Complex_Equation.mw

 

 

 

Hi,

I get the error message "Error, invalid input: diff expects 2 or more arguments, but received 1" from the following program. Could you please help me? Thank you i,n advance for your help!

som:=0:

for b1 from 10 to 10 by 1 do
for b2 from 1 to 2 by 1 do
for alpha from 0.5 to 0.5 by 0.1 do
for beta from 0.33 to 0.5 by 0.1 do
for c from 1 to 1 by 1 do
for f from 1 to 10 by 1 do
for g from 1 to 10 by 0.1 do
for lambdaj from 0.2 to 0.4 by 0.1 do
for gammaj from 0.2 to 0.4 by 0.1 do

p:='p';

aiSQ:=(alpha*b1)/(alpha*b2+beta*b2+c);
ajSQ:=(beta*b1)/(alpha*b2+beta*b2+c);
UiSQ:=(1/2)*alpha*b1^2*(alpha^2*b2+2*alpha*beta*b2+c*alpha+beta^2*b2+2*beta*c)/(alpha*b2+beta*b2+c)^2;
UjSQ:=(1/2)*beta*b1^2*(alpha^2*b2+2*alpha*beta*b2+2*c*alpha+beta^2*b2+beta*c)/(alpha*b2+beta*b2+c)^2;
USQ:=(1/2)*b1^2*(alpha+beta)*(alpha*b2+beta*b2+2*c)/(alpha*b2+beta*b2+c)^2;
UTSQ:=UiSQ+UjSQ+USQ;

ai:=(-alpha*b2*f*p+alpha*b1*c-b2*f*p+b1*c)/(c*(alpha*b2+b2*beta+b2+c));
aj:=(alpha*b2*f*p+b1*beta*c+b2*f*p+c*f*p)/(c*(alpha*b2+b2*beta+b2+c));

aineg:=-(alpha*b2*f*lambdaj*p+b2*f*lambdaj*p+alpha*b1*c+b1*c)/(c*(alpha*b2*lambdaj-2*alpha*b2-b2*beta+b2*lambdaj-2*b2-c));
ajneg:=(alpha*b2*f*lambdaj*p+alpha*b1*c*lambdaj+b2*f*lambdaj*p+c*f*lambdaj*p-alpha*b1*c-b1*beta*c+b1*c*lambdaj-b1*c)/(c*(alpha*b2*lambdaj-2*alpha*b2-b2*beta+b2*lambdaj-2*b2-c));
uj:=beta*(b1*(aineg+ajneg)-(b2/2)*(aineg+ajneg)^2)-(c/2)*ajneg^2-p*f*(ajneg-aj);
uL:=(alpha+1)*(b1*(aineg+ajneg)-(b2/2)*(aineg+ajneg)^2)-(c/2)*aineg^2+p*f*(ajneg-aj);
eqtj:=gammaj*(uL-USQ)-((1-gammaj)/(1-lambdaj))*(uj-UjSQ)-tj;
tj:=solve(eqtj,tj);

dai:=diff(ai,p);
daj:=diff(aj,p);
daineg:=diff(aineg,p);
dajneg:=diff(ajneg,p);
dtj:=diff(tj,p);
Ujp:=beta*(b1*(ai+aj)-(b2/2)*(ai+aj)^2)-(c/2)*aj^2-p*f*(ajneg-aj)+(1-lambdaj)*tj;
ULp:=(alpha+1)*(b1*(ai+aj)-(b2/2)*(ai+aj)^2)-(c/2)*ai^2+p*f*(ajneg-aj)-tj-g*((p^2)/2);
eqp:=diff(ULp,p);
eqpp:=diff(eqp,p);
p:=solve(eqp,p);

CSQ:=b1-b2*(aiSQ+ajSQ);
Cabat:=b1-b2*(ai+aj);
Cneg:=b1-b2*(aineg+ajneg);

if (ai>aineg) then f*(aineg-ai)=0
else if (aj>ajneg) then f*(ajneg-aj)=0
else if (CSQ>0 and Cabat>0  and Cneg>0 and eqpp<0 and p>0 and p<1 and beta<alpha and aiSQ>0 and ajSQ>0 and ai>0 and aj>0 and aineg>0 and ajneg>0 and tj>0)
then
#print(b1,b2,alpha,beta,c,f,g,lambdaj,gammaj,p);
som:=som+1;
fi;fi;fi;
od;od;od;od;od;od;od;od;od;
som;
 

How to make maple sheet background transparent?

and change word color ?

 

A simple (?)  int and too many levels of recursion

 

J := Int(cos(2*x)/(1+2*sin(3*x)^2), x = 0 .. Pi);

Int(cos(2*x)/(1+2*sin(3*x)^2), x = 0 .. Pi)

(1)

evalf[30](J);

-0.321451052376028387436461558651e-32

(2)

value(J);

Error, (in csgn) too many levels of recursion

 

 

 

The workaround I know (for J = 0) it is not very simple.
Can you find an easy one?

 

 

Download int-too-many-levels-of-recursion.mw

how can the graphic as .EPS

f(x,y)=sin(x)*cos(x) , -1<x,y<1

Hello again, I posted a thread here earlier and received some great responses. I've made some progress in Maple since then but once again I've ended up on a question where I am completely stuck. I am only meant to solve this one in maple as the answer is written below the question. The question is:

https://imgur.com/rhFNh2l

I realise this is alot to ask for but I'm studying from afar and I don't have as many options for help as other students at the moment. I have managed to solve a), and I know how to solve b) the traditional way (pen and paper), but I have no idea how to do it in maple. My solution for a) is attached below. c) and d) strictly rely on the answer from b) so I'd greatly appreciate if I could have some help with it so I atleast could attempt the others on my own. This is the final question I have so once I'm done with this I'll pretty much be a master Maple... or not.. :P

I have commented the maple document so it is easier to understand what I've done and what I want help with. Also, I very much apologise if something that I write don't make sense, English is not my native language.

 


 

 

Hello, I just started working in Maple and I am struggling with a question that I found in my book. The question goes as follows:

Consider the set of vectors T = {v1, v2, v3​​​​, v4} in ℝwith

v= (2,5,-2,0), v2 = (-2,-4,b,4), v3 = (-1,2,-2,-5), v= (b,2,5,3)

Find all values of b, such that T is a linearly independent set

I am supposed to first solve it by hand and then in maple. I can solve it by hand but I have no clue how to do it in maple.The only thing I've done so far is create a matrix that contains the vectors in the set S as column entries.

I know that the columns of A are linearly independent if  det A ≠ 0. This is where my near non-existent knowledge in Maple stops me...

The answer is for all {2}

I appreciate any tips...

 

 

Hi maple users

I'm about to do an assignment on the Joukowski transformation, where I have modelled and airfoil resembling the NACA-64015 airfoil. The parameters of the circle in z-plane are as follows: r=1.1241, x=-0.1241, y=0.0, where r is the radius of the circle, and x and y is the parameters used to offset the center of the circle. The problem is that I can't seem to plot the airfoil with contuours showing the fluid flow. I would therefore like to know if any of you guys has solved this before? Any help is much appreciated.

I have a function as below,


 

``

restart

II := 11:

Wij := Matrix(12, 12, {(1, 1) = -.745909803077121, (1, 2) = -0.674461080069867e-2, (1, 3) = .834708547865408, (1, 4) = 0.877385723822038e-2, (1, 5) = -0.908081081472752e-1, (1, 6) = -0.239340836231797e-2, (1, 7) = 0.191800718112554e-2, (1, 8) = 0.418141771959862e-3, (1, 9) = 0.146623811902983e-3, (1, 10) = -0.588304624666211e-4, (1, 11) = -0.556596641532947e-4, (1, 12) = 0.483545553955535e-5, (2, 1) = -0.150780560642874e-2, (2, 2) = 0.867791918452209e-3, (2, 3) = 0.153733767594070e-2, (2, 4) = -0.204845456630398e-1, (2, 5) = -0.637707566405370e-4, (2, 6) = 0.212481474445345e-1, (2, 7) = 0.230866935460358e-4, (2, 8) = -0.263384023057254e-2, (2, 9) = 0.173129262456175e-4, (2, 10) = 0.145986418012667e-2, (2, 11) = -0.615768525233225e-5, (2, 12) = -0.455559328816086e-3, (3, 1) = 1.07234104621714, (3, 2) = 0.971025800610391e-2, (3, 3) = -1.19283486996676, (3, 4) = -0.126396150015806e-1, (3, 5) = .118988853710128, (3, 6) = 0.340933797889320e-2, (3, 7) = 0.190278053641238e-2, (3, 8) = -0.565664886428382e-3, (3, 9) = -0.503156502649439e-3, (3, 10) = 0.979522657647879e-4, (3, 11) = 0.113002768409814e-3, (3, 12) = -0.121533604250274e-4, (4, 1) = 0.245302677746526e-2, (4, 2) = 0.611598278493220e-3, (4, 3) = -0.251651574609684e-2, (4, 4) = 0.278857618849383e-1, (4, 5) = 0.108022265014592e-3, (4, 6) = -0.320168363280661e-1, (4, 7) = -0.325097140040140e-4, (4, 8) = 0.480517189034762e-2, (4, 9) = -0.193985210422571e-4, (4, 10) = -0.190626072415250e-2, (4, 11) = 0.739266431705442e-5, (4, 12) = 0.619688407885468e-3, (5, 1) = -.332680012459335, (5, 2) = -0.308899427286697e-2, (5, 3) = .359841697913305, (5, 4) = 0.403401520601850e-2, (5, 5) = -0.200704409346196e-1, (5, 6) = -0.104338164548124e-2, (5, 7) = -0.748747318317741e-2, (5, 8) = 0.123603846422314e-3, (5, 9) = 0.587068975361258e-3, (5, 10) = -0.290076105262677e-4, (5, 11) = -0.191603816451559e-3, (5, 12) = 0.373388286597686e-5, (6, 1) = -0.103361884660837e-2, (6, 2) = -0.295276339713243e-2, (6, 3) = 0.108951918505810e-2, (6, 4) = -0.479183265920926e-2, (6, 5) = -0.592008998858512e-4, (6, 6) = 0.102437161326541e-1, (6, 7) = 0.859907872385912e-5, (6, 8) = -0.266521683446180e-2, (6, 9) = -0.383709478639487e-5, (6, 10) = 0.266632726737390e-3, (6, 11) = -0.148469080898987e-5, (6, 12) = -0.101665157432172e-3, (7, 1) = 0.703379342372258e-2, (7, 2) = 0.176251183163216e-3, (7, 3) = -0.145630485079540e-2, (7, 4) = -0.233067786529769e-3, (7, 5) = -0.922702754264408e-2, (7, 6) = 0.364384299428906e-4, (7, 7) = 0.417281143846606e-2, (7, 8) = 0.324111696921334e-4, (7, 9) = -0.484660014401307e-3, (7, 10) = -0.128619131156994e-4, (7, 11) = -0.412616528382663e-4, (7, 12) = 0.7982985444e-6, (8, 1) = 0.974187082179976e-4, (8, 2) = 0.155548383221531e-2, (8, 3) = -0.123838922170996e-3, (8, 4) = -0.249773787243565e-2, (8, 5) = 0.221867864063737e-4, (8, 6) = 0.480516696280202e-3, (8, 7) = -0.359606407557896e-5, (8, 8) = 0.433976774887701e-3, (8, 9) = 0.811301081325245e-5, (8, 10) = 0.727673884033783e-4, (8, 11) = -0.3022512840e-6, (8, 12) = -0.468064718553966e-4, (9, 1) = -0.682570264341669e-3, (9, 2) = -0.587007804372093e-4, (9, 3) = -0.666643577308233e-3, (9, 4) = 0.662778988863377e-4, (9, 5) = 0.125271290023062e-2, (9, 6) = -0.232225466973706e-5, (9, 7) = -0.410694230883052e-3, (9, 8) = -0.106713819648935e-4, (9, 9) = 0.366616746138017e-3, (9, 10) = 0.217010277855600e-5, (9, 11) = 0.135713097667273e-3, (9, 12) = 0.320410261333838e-5, (10, 1) = -0.101818162719231e-4, (10, 2) = -0.157599695320146e-3, (10, 3) = 0.929732652373664e-5, (10, 4) = -0.189234110745728e-3, (10, 5) = -0.859354584213451e-5, (10, 6) = 0.214578509593470e-4, (10, 7) = 0.613328774334630e-5, (10, 8) = 0.117712820070324e-3, (10, 9) = -0.213534503887478e-5, (10, 10) = 0.179089799811260e-3, (10, 11) = 0.546912773241878e-5, (10, 12) = 0.273197376236470e-4, (11, 1) = -0.108150650095191e-3, (11, 2) = 0.568807678432329e-5, (11, 3) = 0.416808900313591e-3, (11, 4) = -0.132889420052041e-5, (11, 5) = -0.136041936047118e-3, (11, 6) = -0.673784027004257e-5, (11, 7) = -0.942090825967484e-4, (11, 8) = 0.222185688977502e-5, (11, 9) = -0.113443667198581e-3, (11, 10) = 0.6962003263e-6, (11, 11) = 0.361765818744130e-4, (11, 12) = -0.5344899574e-6, (12, 1) = 0.112445517997156e-5, (12, 2) = 0.741957037817598e-4, (12, 3) = 0.420901487126838e-5, (12, 4) = 0.763065573748303e-4, (12, 5) = 0.136237864072227e-5, (12, 6) = 0.239279022456648e-4, (12, 7) = -0.171222080223248e-5, (12, 8) = -0.577109791933568e-4, (12, 9) = -0.3869218336e-7, (12, 10) = -0.715889637469861e-4, (12, 11) = -0.491358853466192e-5, (12, 12) = -0.419960052327950e-4})

Wij := Matrix(12, 12, {(1, 1) = -.745909803077121, (1, 2) = -0.674461080069867e-2, (1, 3) = .834708547865408, (1, 4) = 0.877385723822038e-2, (1, 5) = -0.908081081472752e-1, (1, 6) = -0.239340836231797e-2, (1, 7) = 0.191800718112554e-2, (1, 8) = 0.418141771959862e-3, (1, 9) = 0.146623811902983e-3, (1, 10) = -0.588304624666211e-4, (1, 11) = -0.556596641532947e-4, (1, 12) = 0.483545553955535e-5, (2, 1) = -0.150780560642874e-2, (2, 2) = 0.867791918452209e-3, (2, 3) = 0.153733767594070e-2, (2, 4) = -0.204845456630398e-1, (2, 5) = -0.637707566405370e-4, (2, 6) = 0.212481474445345e-1, (2, 7) = 0.230866935460358e-4, (2, 8) = -0.263384023057254e-2, (2, 9) = 0.173129262456175e-4, (2, 10) = 0.145986418012667e-2, (2, 11) = -0.615768525233225e-5, (2, 12) = -0.455559328816086e-3, (3, 1) = 1.07234104621714, (3, 2) = 0.971025800610391e-2, (3, 3) = -1.19283486996676, (3, 4) = -0.126396150015806e-1, (3, 5) = .118988853710128, (3, 6) = 0.340933797889320e-2, (3, 7) = 0.190278053641238e-2, (3, 8) = -0.565664886428382e-3, (3, 9) = -0.503156502649439e-3, (3, 10) = 0.979522657647879e-4, (3, 11) = 0.113002768409814e-3, (3, 12) = -0.121533604250274e-4, (4, 1) = 0.245302677746526e-2, (4, 2) = 0.611598278493220e-3, (4, 3) = -0.251651574609684e-2, (4, 4) = 0.278857618849383e-1, (4, 5) = 0.108022265014592e-3, (4, 6) = -0.320168363280661e-1, (4, 7) = -0.325097140040140e-4, (4, 8) = 0.480517189034762e-2, (4, 9) = -0.193985210422571e-4, (4, 10) = -0.190626072415250e-2, (4, 11) = 0.739266431705442e-5, (4, 12) = 0.619688407885468e-3, (5, 1) = -.332680012459335, (5, 2) = -0.308899427286697e-2, (5, 3) = .359841697913305, (5, 4) = 0.403401520601850e-2, (5, 5) = -0.200704409346196e-1, (5, 6) = -0.104338164548124e-2, (5, 7) = -0.748747318317741e-2, (5, 8) = 0.123603846422314e-3, (5, 9) = 0.587068975361258e-3, (5, 10) = -0.290076105262677e-4, (5, 11) = -0.191603816451559e-3, (5, 12) = 0.373388286597686e-5, (6, 1) = -0.103361884660837e-2, (6, 2) = -0.295276339713243e-2, (6, 3) = 0.108951918505810e-2, (6, 4) = -0.479183265920926e-2, (6, 5) = -0.592008998858512e-4, (6, 6) = 0.102437161326541e-1, (6, 7) = 0.859907872385912e-5, (6, 8) = -0.266521683446180e-2, (6, 9) = -0.383709478639487e-5, (6, 10) = 0.266632726737390e-3, (6, 11) = -0.148469080898987e-5, (6, 12) = -0.101665157432172e-3, (7, 1) = 0.703379342372258e-2, (7, 2) = 0.176251183163216e-3, (7, 3) = -0.145630485079540e-2, (7, 4) = -0.233067786529769e-3, (7, 5) = -0.922702754264408e-2, (7, 6) = 0.364384299428906e-4, (7, 7) = 0.417281143846606e-2, (7, 8) = 0.324111696921334e-4, (7, 9) = -0.484660014401307e-3, (7, 10) = -0.128619131156994e-4, (7, 11) = -0.412616528382663e-4, (7, 12) = 0.798298544439708e-6, (8, 1) = 0.974187082179976e-4, (8, 2) = 0.155548383221531e-2, (8, 3) = -0.123838922170996e-3, (8, 4) = -0.249773787243565e-2, (8, 5) = 0.221867864063737e-4, (8, 6) = 0.480516696280202e-3, (8, 7) = -0.359606407557896e-5, (8, 8) = 0.433976774887701e-3, (8, 9) = 0.811301081325245e-5, (8, 10) = 0.727673884033783e-4, (8, 11) = -0.302251283982269e-6, (8, 12) = -0.468064718553966e-4, (9, 1) = -0.682570264341669e-3, (9, 2) = -0.587007804372093e-4, (9, 3) = -0.666643577308233e-3, (9, 4) = 0.662778988863377e-4, (9, 5) = 0.125271290023062e-2, (9, 6) = -0.232225466973706e-5, (9, 7) = -0.410694230883052e-3, (9, 8) = -0.106713819648935e-4, (9, 9) = 0.366616746138017e-3, (9, 10) = 0.217010277855600e-5, (9, 11) = 0.135713097667273e-3, (9, 12) = 0.320410261333838e-5, (10, 1) = -0.101818162719231e-4, (10, 2) = -0.157599695320146e-3, (10, 3) = 0.929732652373664e-5, (10, 4) = -0.189234110745728e-3, (10, 5) = -0.859354584213451e-5, (10, 6) = 0.214578509593470e-4, (10, 7) = 0.613328774334630e-5, (10, 8) = 0.117712820070324e-3, (10, 9) = -0.213534503887478e-5, (10, 10) = 0.179089799811260e-3, (10, 11) = 0.546912773241878e-5, (10, 12) = 0.273197376236470e-4, (11, 1) = -0.108150650095191e-3, (11, 2) = 0.568807678432329e-5, (11, 3) = 0.416808900313591e-3, (11, 4) = -0.132889420052041e-5, (11, 5) = -0.136041936047118e-3, (11, 6) = -0.673784027004257e-5, (11, 7) = -0.942090825967484e-4, (11, 8) = 0.222185688977502e-5, (11, 9) = -0.113443667198581e-3, (11, 10) = 0.696200326268231e-6, (11, 11) = 0.361765818744130e-4, (11, 12) = -0.534489957398908e-6, (12, 1) = 0.112445517997156e-5, (12, 2) = 0.741957037817598e-4, (12, 3) = 0.420901487126838e-5, (12, 4) = 0.763065573748303e-4, (12, 5) = 0.136237864072227e-5, (12, 6) = 0.239279022456648e-4, (12, 7) = -0.171222080223248e-5, (12, 8) = -0.577109791933568e-4, (12, 9) = -0.386921833637950e-7, (12, 10) = -0.715889637469861e-4, (12, 11) = -0.491358853466192e-5, (12, 12) = -0.419960052327950e-4})

(1)

Wxy1 := add(add(h*Wij[i+1, j+1]*LegendreP(i, Zeta)*LegendreP(j, eta), i = 0 .. II), j = 0 .. JJ):

Wxy[1] := simplify(Wxy1):

Plt := plot3d(Wxy[1], Zeta = -1 .. 1, eta = -1 .. 1)

 

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How I can normalize it in range [0,1]

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